Fused filament fabrication (FFF) is one of the most popular additive manufacturing (AM) processes that utilize thermoplastic polymers to produce three-dimensional (3D) geometry products. The FFF filament materials have a significant role in determining the properties of the final part produced, such as mechanical properties, thermal conductivity, and electrical conductivity. This article intensively reviews the state-of-the-art materials for FFF filaments. To date, there are many different types of FFF filament materials that have been developed. The filament materials range from pure thermoplastics to composites, bioplastics, and composites of bioplastics. Different types of reinforcements such as particles, fibers, and nanoparticles are incorporated into the composite filaments to improve the FFF build part properties. The performance, limitations, and opportunities of a specific type of FFF filament will be discussed. Additionally, the challenges and requirements for filament production from different materials will be evaluated. In addition, to provide a concise review of fundamental knowledge about the FFF filament, this article will also highlight potential research directions to stimulate future filament development. Finally, the importance and scopes of using bioplastics and their composites for developing eco-friendly filaments will be introduced.